Abstract

We present an analytic method to approach Eilenberger equation and the associated Bogoliubov–de Gennes equation for quasi-1D fermionic gases. The problem of finding self-consistent inhomogeneous condensates is reduced to solving a certain class of nonlinear Schrödinger equations, whose most general solitonic solution is indeed available. Previously known solutions can be retrieved by taking appropriate limits in the parameters. The applicability of the method extends to systems with population imbalance and subject to external potential. In particular we show that fermionic zero-modes are robust against population imbalance.

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Acknowledgements

The work of GM is supported by a RIKEN FPR fellowship. The work of MN is supported in part by a Grant-in-Aid for Scientific Research (No. 25400268) and by the “Topological Quantum Phenomena” Grant-in-Aid for Scientific Research on Innovative Areas (No. 25103720) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. ST was supported by Grant-in-Aid for Scientific Research, No. 24740276. R. Y. is the Yukawa Fellow and this work is partially supported by Yukawa Memorial Foundation.